Shadow isn't casted on object
I made a similair setup and it seems to work for me.

As you can see, I also made use of a light source and put this inside the Sun sphere. There Are several things you need to check.

1) First of all you need to ensure if your light source has shadows enabled. You can check that out in the next image. Select your light source.



2) If you also decide to have the light source inside your Sun, you need to make sure the shadow of the Sun sphere is disabled as seen in the next image. Select your Sun.



3) Third thing to make sure is that you planet is casting the shadows on the rings. See here:



I've added a copy of the blend file:



Hope this helps!